We are asked to find the equation of a line that passes through the point $(4, 5)$ and is parallel to the line $y = x - 1$. The answer choices are given as multiple choice options.

1. Problem Description

We are asked to find the equation of a line that passes through the point $(4, 5)$ and is parallel to the line $y = x - 1$. The answer choices are given as multiple choice options.

2. Solution Steps

The equation of a line can be written in the slope-intercept form as:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

Since the line we are looking for is parallel to the line $y = x - 1$, the slope of our line is the same as the slope of the given line. In the equation $y = x - 1$, the coefficient of $x$ is $1$, so the slope is $m = 1$.

Thus, the equation of our line is of the form $y = 1x + b$, or $y = x + b$.

We are given that the line passes through the point $(4, 5)$. This means that when $x = 4$, $y = 5$. We can substitute these values into our equation to solve for $b$:

$5 = 4 + b$

$b = 5 - 4$

$b = 1$

Therefore, the equation of the line is $y = x + 1$.

3. Final Answer

The equation of the line is $y = x + 1$. The answer is (b).